Artículo
Rossi, J.D.; Saez, M. "Optimal regularity for the pseudo infinity Laplacian" (2007) ESAIM - Control, Optimisation and Calculus of Variations. 13(2):294-304
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Abstract:
In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity Laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem. © EDP Sciences, SMAI 2007.
Registro:
| Documento: | Artículo |
| Título: | Optimal regularity for the pseudo infinity Laplacian |
| Autor: | Rossi, J.D.; Saez, M. |
| Filiación: | Instituto de Matemáticas y Física, Fundamental Consejo Superior de Investigaciones, Científicas Serrano 123, Madrid, Spain Departamento de Matemática, FCEyN UBA, (1428) Buenos Aires, Argentina Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, 14476 Golm, Germany |
| Palabras clave: | Optimal regularity; Pseudo infinity Laplacian; Viscosity solutions; Laplace equation; Problem solving; Viscosity; Optimal regularity; Pseudo infinity Laplacian; Viscosity solutions; Optimal control systems |
| Año: | 2007 |
| Volumen: | 13 |
| Número: | 2 |
| Página de inicio: | 294 |
| Página de fin: | 304 |
| DOI: | http://dx.doi.org/10.1051/cocv:2007018 |
| Título revista: | ESAIM - Control, Optimisation and Calculus of Variations |
| Título revista abreviado: | Control Optimisation Calc. Var. |
| ISSN: | 12928119 |
| CODEN: | ECOVF |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_12928119_v13_n2_p294_Rossi.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12928119_v13_n2_p294_Rossi |
Referencias:
- Aronsson, G., Extensions of functions satisflying Lipschitz conditions (1967) Ark. Math, 6, pp. 551-561
- Aronsson, G., Crandall, M.G., Juutinen, P., A tour of the theory of absolutely minimizing functions (2004) Bull. Amer. Math. Soc, 41, pp. 439-505
- Barles, G., Busca, J., Existence and comparison results for fully nonlinear degenerate elliptic equations without zeroth-order term (2001) Comm. Part. Diff. Eq, 26, pp. 2323-2337
- Belloni, M., Kawohl, B., The pseudo-p-Laplace eigenvalue problem and viscosity solutions as p → ∞ (2004) ESAIM: COCV, 10, pp. 28-52
- Belloni, M., Kawohl, B., Juutinen, P., The p-Laplace eigenvalue problem as p → ∞ in a Finsler metric J. Europ. Math. Soc. (to appear)
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- Crandall, M.G., Ishii, H., Lions, P.L., User's guide to viscosity solutions of second order partial differential equations (1992) Bull. Amer. Math. Soc, 27, pp. 1-67
- Crandall, M.G., Evans, L.C., Gariepy, R.F., Optimal Lipschitz extensions and the infinity Laplacian (2001) Calc. Var. PDE, 13, pp. 123-139
- Evans, L.C., Gangbo, W., Differential equations methods for the Monge-Kantorovich mass transfer problem (1999) Mem. Amer. Math. Soc, 137 (653)
- Jensen, R., Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient (1993) Arch. Rational Mech. Anal, 123, pp. 51-74
- Savin, O., C1 regularity for infinity harmonic functions in two dimensions (2005) Arch. Rational Mech. Anal, 176, pp. 351-361
Citas:
---------- APA ----------
Rossi, J.D. & Saez, M. (2007) . Optimal regularity for the pseudo infinity Laplacian. ESAIM - Control, Optimisation and Calculus of Variations, 13(2), 294-304.http://dx.doi.org/10.1051/cocv:2007018
---------- CHICAGO ----------
Rossi, J.D., Saez, M. "Optimal regularity for the pseudo infinity Laplacian" . ESAIM - Control, Optimisation and Calculus of Variations 13, no. 2 (2007) : 294-304.http://dx.doi.org/10.1051/cocv:2007018
---------- MLA ----------
Rossi, J.D., Saez, M. "Optimal regularity for the pseudo infinity Laplacian" . ESAIM - Control, Optimisation and Calculus of Variations, vol. 13, no. 2, 2007, pp. 294-304.http://dx.doi.org/10.1051/cocv:2007018
---------- VANCOUVER ----------
Rossi, J.D., Saez, M. Optimal regularity for the pseudo infinity Laplacian. Control Optimisation Calc. Var. 2007;13(2):294-304.http://dx.doi.org/10.1051/cocv:2007018
